CS345 Data Mining
Link Analysis 2: Topic-Specific Page Rank Hubs and Authorities Spam Detection
Anand Rajaraman, Jeffrey D. Ullman Some problems with page rank
Measures generic popularity of a page Biased against topic-specific authorities Ambiguous queries e.g., jaguar Uses a single measure of importance Other models e.g., hubs-and-authorities Susceptible to Link spam Artificial link topographies created in order to boost page rank Topic-Specific Page Rank
Instead of generic popularity, can we measure popularity within a topic? E.g., computer science, health Bias the random walk When the random walker teleports, he picks a page from a set S of web pages S contains only pages that are relevant to the topic E.g., Open Directory (DMOZ) pages for a given topic (www.dmoz.org ) For each teleport set S, we get a different rank vector rS Matrix formulation
2 Aij = βMij + (1-β)/|S| if i S
Aij = βMij otherwise Show that A is stochastic We have weighted all pages in the teleport set S equally Could also assign different weights to them Example
0.2 Suppose S = {1}, β = 0.8 0.5 1 0.4 0.5 0.4 1 0.8 2 3
1 1 0.8 0.8 Node Iteration 0 1 2… stable 4 1 1.0 0.2 0.52 0.294 2 0 0.4 0.08 0.118 3 0 0.4 0.08 0.327 4 0 0 0.32 0.261
Note how we initialize the page rank vector differently from the unbiased page rank case. How well does TSPR work?
Experimental results [Haveliwala 2000] Picked 16 topics Teleport sets determined using DMOZ E.g., arts, business, sports,… “Blind study” using volunteers 35 test queries Results ranked using Page Rank and TSPR of most closely related topic E.g., bicycling using Sports ranking In most cases volunteers preferred TSPR ranking Which topic ranking to use?
User can pick from a menu Use Bayesian classification schemes to classify query into a topic Can use the context of the query E.g., query is launched from a web page talking about a known topic History of queries e.g., “basketball” followed by “jordan” User context e.g., user’s My Yahoo settings, bookmarks, … Hubs and Authorities
Suppose we are given a collection of documents on some broad topic e.g., stanford, evolution, iraq perhaps obtained through a text search Can we organize these documents in some manner? Page rank offers one solution HITS (Hypertext-Induced Topic Selection) is another proposed at approx the same time (1998) HITS Model
Interesting documents fall into two classes Authorities are pages containing useful information course home pages home pages of auto manufacturers Hubs are pages that link to authorities course bulletin list of US auto manufacturers Idealized view
Hubs Authorities Mutually recursive definition
A good hub links to many good authorities A good authority is linked from many good hubs Model using two scores for each node Hub score and Authority score Represented as vectors h and a Transition Matrix A
HITS uses a matrix A[i, j] = 1 if page i links to page j, 0 if not AT, the transpose of A, is similar to the PageRank matrix M, but AT has 1’s where M has fractions Example
y a m Yahoo y 1 1 1 A = a 1 0 1 m 0 1 0
Amazon M’soft Hub and Authority Equations
The hub score of page P is proportional to the sum of the authority scores of the pages it links to h = λAa Constant λ is a scale factor The authority score of page P is proportional to the sum of the hub scores of the pages it is linked from a = µAT h Constant µ is scale factor Iterative algorithm
Initialize h, a to all 1’s h = Aa Scale h so that its max entry is 1.0 a = ATh Scale a so that its max entry is 1.0 Continue until h, a converge Example
1 1 1 1 1 0 A = 1 0 1 AT = 1 0 1 0 1 0 1 1 0
a(yahoo) = 1 1 1 1 . . . 1 a(amazon) = 1 1 4/5 0.75 . . . 0.732 a(m’soft) = 1 1 1 1 . . . 1
h(yahoo) = 1 1 1 1 . . . 1.000 h(amazon) = 1 2/3 0.71 0.73 . . . 0.732 h(m’soft) = 1 1/3 0.29 0.27 . . . 0.268 Existence and Uniqueness h = λAa a = µAT h h = λµ AA T h a = λµ ATA a
Under reasonable assumptions about A, the dual iterative algorithm converges to vectors h* and a* such that: • h* is the principal eigenvector of the matrix AA T • a* is the principal eigenvector of the matrix ATA Bipartite cores
Hubs Authorities
Most densely-connected core (primary core )
Less densely-connected core (secondary core ) Secondary cores
A single topic can have many bipartite cores corresponding to different meanings, or points of view abortion: pro-choice, pro-life evolution: darwinian, intelligent design jaguar: auto, Mac, NFL team, panthera onca How to find such secondary cores? Non-primary eigenvectors
AA T and ATA have the same set of eigenvalues An eigenpair is the pair of eigenvectors with the same eigenvalue The primary eigenpair (largest eigenvalue) is what we get from the iterative algorithm Non-primary eigenpairs correspond to other bipartite cores The eigenvalue is a measure of the density of links in the core Finding secondary cores
Once we find the primary core, we can remove its links from the graph Repeat HITS algorithm on residual graph to find the next bipartite core Technically, not exactly equivalent to non-primary eigenpair model Creating the graph for HITS
We need a well-connected graph of pages for HITS to work well Page Rank and HITS
Page Rank and HITS are two solutions to the same problem What is the value of an inlink from S to D? In the page rank model, the value of the link depends on the links into S In the HITS model, it depends on the value of the other links out of S The destinies of Page Rank and HITS post-1998 were very different Why? Web Spam
Search has become the default gateway to the web Very high premium to appear on the first page of search results e.g., e-commerce sites advertising-driven sites What is web spam?
Spamming = any deliberate action solely in order to boost a web page’s position in search engine results, incommensurate with page’s real value Spam = web pages that are the result of spamming This is a very broad defintion SEO industry might disagree! SEO = search engine optimization Approximately 10-15% of web pages are spam Web Spam Taxonomy
We follow the treatment by Gyongyi and Garcia-Molina [2004] Boosting techniques Techniques for achieving high relevance/importance for a web page Hiding techniques Techniques to hide the use of boosting From humans and web crawlers Boosting techniques
Term spamming Manipulating the text of web pages in order to appear relevant to queries Link spamming Creating link structures that boost page rank or hubs and authorities scores Term Spamming
Repetition of one or a few specific terms e.g., free, cheap, viagra Goal is to subvert TF.IDF ranking schemes Dumping of a large number of unrelated terms e.g., copy entire dictionaries Weaving Copy legitimate pages and insert spam terms at random positions Phrase Stitching Glue together sentences and phrases from different sources Link spam
Three kinds of web pages from a spammer’s point of view Inaccessible pages Accessible pages e.g., web log comments pages spammer can post links to his pages Own pages Completely controlled by spammer May span multiple domain names Link Farms
Spammer’s goal Maximize the page rank of target page t Technique Get as many links from accessible pages as possible to target page t Construct “link farm” to get page rank multiplier effect Link Farms
Accessible Own
1 InaccessibleInaccessible 2 t
M
One of the most common and effective organizations for a link farm Analysis
Accessible Own 1 Inaccessible Inaccessible t 2
M Suppose rank contributed by accessible pages = x Let page rank of target page = y Rank of each “farm” page = βy/M + (1-β)/N y = x + βM[ βy/M + (1-β)/N] + (1-β)/N = x + β2y + β(1-β)M/N + (1-β)/N Very small; ignore y = x/(1-β2) + cM/N where c = β/(1+ β) Analysis
Accessible Own 1 Inaccessible Inaccessible t 2
M
y = x/(1-β2) + cM/N where c = β/(1+ β) For β = 0.85, 1/(1-β2)= 3.6 Multiplier effect for “acquired” page rank By making M large, we can make y as large as we want Detecting Spam
Term spamming Analyze text using statistical methods e.g., Naïve Bayes classifiers Similar to email spam filtering Also useful: detecting approximate duplicate pages Link spamming Open research area One approach: TrustRank TrustRank idea
Basic principle: approximate isolation It is rare for a “good” page to point to a “bad” (spam) page Sample a set of “seed pages” from the web Have an oracle (human) identify the good pages and the spam pages in the seed set Expensive task, so must make seed set as small as possible Trust Propagation
Call the subset of seed pages that are identified as “good” the “trusted pages” Set trust of each trusted page to 1 Propagate trust through links Each page gets a trust value between 0 and 1 Use a threshold value and mark all pages below the trust threshold as spam Example
1 2 3 good 4 bad 5 6
7 Rules for trust propagation
Trust attenuation The degree of trust conferred by a trusted page decreases with distance Trust splitting The larger the number of outlinks from a page, the less scrutiny the page author gives each outlink Trust is “split” across outlinks Simple model
Suppose trust of page p is t(p) Set of outlinks O(p) For each q 2O(p), p confers the trust βt(p)/|O(p)| for 0< β<1 Trust is additive Trust of p is the sum of the trust conferred on p by all its inlinked pages Note similarity to Topic-Specific Page Rank Within a scaling factor, trust rank = biased page rank with trusted pages as teleport set Picking the seed set
Two conflicting considerations Human has to inspect each seed page, so seed set must be as small as possible Must ensure every “good page” gets adequate trust rank, so need make all good pages reachable from seed set by short paths Approaches to picking seed set
Suppose we want to pick a seed set of k pages PageRank Pick the top k pages by page rank Assume high page rank pages are close to other highly ranked pages We care more about high page rank “good” pages Inverse page rank
Pick the pages with the maximum number of outlinks Can make it recursive Pick pages that link to pages with many outlinks Formalize as “inverse page rank” Construct graph G’ by reversing each edge in web graph G Page Rank in G’ is inverse page rank in G Pick top k pages by inverse page rank Spam Mass
In the TrustRank model, we start with good pages and propagate trust Complementary view: what fraction of a page’s page rank comes from “spam” pages? In practice, we don’t know all the spam pages, so we need to estimate Spam mass estimation r(p) = page rank of page p r+(p) = page rank of p with teleport into “good” pages only r-(p) = r(p) – r+(p) Spam mass of p = r-(p)/r(p) Good pages
For spam mass, we need a large set of “good” pages Need not be as careful about quality of individual pages as with TrustRank One reasonable approach .edu sites .gov sites .mil sites Another approach
Backflow from known spam pages Course project from last year’s edition of this course Still an open area of research…